Cut-ups
Simple as it is, I liked the game design challenge mentioned below so much that it completely overwhelmed the post. So I cut it up.
The random or pseudo-random juxtaposition of elements is an excellent way of stimulating creativity and discovery. An exercise I once did with some friends in France over lunch involved taking a game genre and a fictional universe (in our particular case, one of the universes developed by our company) and trying to design a game incorporating both. I have repeated this at other times; it's interesting to see the different ideas people come up with when they're inventing a racing game set in the Nightmare Creatures universe.
The cut-up technique, made famous by William Burroughs, can be used in a similar way, even though Burroughs allegedly used it to subvert the insects from another planet that were possibly controlling his mind. (You may want to omit this information when trying to convince others to apply this technique.)
Links: An interview with William Burroughs mentioning the cut-up technique (but not the mind-controlling insects). A web page about Burroughs and cut-up.